Problem: Solve for $x$ and $y$ using elimination. ${-2x-y = -17}$ ${-5x+y = -32}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-7x = -49$ $\dfrac{-7x}{{-7}} = \dfrac{-49}{{-7}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-2x-y = -17}\thinspace$ to find $y$ ${-2}{(7)}{ - y = -17}$ $-14-y = -17$ $-14{+14} - y = -17{+14}$ $-y = -3$ $\dfrac{-y}{{-1}} = \dfrac{-3}{{-1}}$ ${y = 3}$ You can also plug ${x = 7}$ into $\thinspace {-5x+y = -32}\thinspace$ and get the same answer for $y$ : ${-5}{(7)}{ + y = -32}$ ${y = 3}$